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Question 1103141: A helicopter is descending at a constant rate. In the table, t represents the number of minutes since the helicopter began its descent. The helicopter's elevation in feet at time t is represented by f(t). At what rate does the helicopter's elevation change?
t=1,3,6,10
f(t)=6480,5740,4630,3150
A. -370 ft/mi
B. -460 ft/mi
C. -770 ft/mi
D. -245 ft/mi
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! at t = 1, the elevation is 6480
at t = 3, the elevation is 5740
at t = 6, the elevation is 4630
at t = 3150, the elevation is 3150.
you are given that the plane descends at a constant rate.
this is equivalent to a linear rate and so a linear equation applies.
the slope intercept form of the linear equation is y = mx + b.
m is the slope
b is the y-intercept.
the slope is equal to (y2-y1) / (x2-x1)
x1 and x2 are randomly chosen points on the line which means they both are coordinate pairs that are calculated through the equation.
in your table, the coordinate pairs of (x,y) are equal to (time,elevation) where x represents the number of minutes since the helicopter starts its descent and y represents the elevation at that time.
we'll pick the elevation at 1 minute of the descent and the elevation at 10 minutes of the descent.
this makes (x1,y1) = (1,6480) and (x2,y2) = (10,3150.
m = the slope = (y2-y1) / (x2-x1) = (3150 - 6480) / (10 - 1) = -3330 / 9 = -370.
that's your solution.
to go on a bit further, the slope intercept form of the equation becomes y = -370 * x + b.
to solve for the y-intercept, we replace x and y with one of the coordinates and solve for b.
since any point on the line will do, we'll choose (6,4630).
the equation becomes 4630 = -370 * 6 + b
solve for b to get b = 6850.
the equation now becomes y = -370 * x + 6850.
when t = 0, the elevation is 6850.
this equation can now be graphed and is shown below along with the time at 0, 1, 3, 6, and 10 minutes of descent.
also shown is the amount of time that elapsed when the helicoptor lands, assuming that it continues at the same constant rate until it touches the ground.
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